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Full text of "Mathematical And Physical Papers - Iii"

Two streams thus related may be said to be oppositely polarized. Two streams of plane-polarized light in which the planes of polarization are at right angles to each other, and two streams of circularly polarized light, one right-handed and the other left-handed, are particular cases of streams oppositely polarized.
In the reasoning of this article, nothing depends upon the precise relation between the two polarized streams and the original stream. All that it is necessary to suppose is, that the two polarized streams came originally from the same polarized source, so that the changes in epoch and intensity, that is, the changes in the quantities e, c, are the same for the two streams. Nothing depends upon the precise nature of these changes, which may be either abrupt or continuous, but must be sufficiently infrequent if abrupt, or sufficiently gradual if continuous, to allow of our regarding c and e as constant for a great number of successive undulations. Our results will apply just as well to the disturbance produced by the union of two neighbouring streams coming originally from the same polarized source, but having had their polarizations modified, as to that produced by the union, after recomposition, of the components of a single polarized stream. Since the resulting intensity is independent of S, it follows that two oppositely polarized streams coming originally from the same polarized source are incapable of interfering, but two streams polarized otherwise than oppositely necessarily interfere, to a greater or less degree, when the difference in their retardation of phase is sufficiently small. Of course the interference here spoken of means only that which is exhibited without analyzation.
4. Two interfering streams may be said to interfere perfectly when the fluctuations of intensity are the greatest that the difference in the intensities of the interfering streams admits of, so that in case of equality the minima are absolutely equal to zero. Referring to (9), we see that in order that this may be the case the maximum value of the coefficient of 20^ must be equal to 1. Now the maximum value of A cos 8 -h /3 sin S is V (A* + JB2), and therefore we must have
cos2 («2 - aj cos2 (ft - ft) 4- sin2 («2 - a^ sin'2 (#2+ ft) = 1
= cos2 (a2 - ax) -I- sin2 («2 - aj, s. in.                                                                          16